In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model. This article is part of the theme issue 'Machine learning for weather and climate modelling'.The recent hype about artificial intelligence has sparked renewed interest in applying the successful deep learning (DL) methods for image recognition, speech recognition, robotics, strategic games and other application areas to the field of meteorology. There is some evidence that better weather forecasts can be produced by introducing big data mining and neural networks into the weather prediction workflow. Here, we discuss the question of whether it is possible to completely replace the current numerical weather models and data assimilation systems with DL approaches. This discussion entails a review of state-of-the-art machine learning concepts and their applicability to weather data with its pertinent statistical properties. We think that it is not inconceivable that numerical weather models may one day become obsolete, but a number of fundamental breakthroughs are needed before this goal comes into reach. This article is part of the theme issue 'Machine learning for weather and climate modelling'.Modern weather and climate models share a common heritage and often even components; however, they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should reflect this. While the use of machine learning to emulate weather forecast models is a relatively new endeavour, there is a rich history of climate model emulation. This is primarily because while weather modelling is an initial condition problem, which intimately depends on the current state of the atmosphere, climate modelling is predominantly a boundary condition problem. To emulate the response of the climate to different drivers therefore, representation of the full dynamical evolution of the atmosphere is neither necessary, or in many cases, desirable. Climate scientists are typically interested in different questions also. Indeed emulating the steady-state climate response has been possible for many years and provides significant speed increases that allow solving inverse problems for e.g. parameter estimation. Nevertheless, the large datasets, non-linear relationships and limited training data make climate a domain which is rich in interesting machine learning challenges. Here, I seek to set out the current state of climate model emulation and demonstrate how, despite some challenges, recent advances in machine learning provide new opportunities for creating useful statistical models of the climate. This article is part of the theme issue 'Machine learning for weather and climate modelling'.The most mature aspect of applying artificial intelligence (AI)/machine learning (ML) to problems in the atmospheric sciences is likely post-processing of model output. This article provides some history and current state of the science of post-processing with AI for weather and climate models. Deriving from the discussion at the 2019 Oxford workshop on Machine Learning for Weather and Climate, this paper also presents thoughts on medium-term goals to advance such use of AI, which include assuring that algorithms are trustworthy and interpretable, adherence to FAIR data practices to promote usability, and development of techniques that leverage our physical knowledge of the atmosphere. The coauthors propose several actionable items and have initiated one of those a repository for datasets from various real weather and climate problems that can be addressed using AI. Five such datasets are presented and permanently archived, together with Jupyter notebooks to process them and assess the results in comparison with a baseline technique. The coauthors invite the readers to test their own algorithms in comparison with the baseline and to archive their results. This article is part of the theme issue 'Machine learning for weather and climate modelling'.Quantifying uncertainty in weather forecasts is critical, especially for predicting extreme weather events. This is typically accomplished with ensemble prediction systems, which consist of many perturbed numerical weather simulations, or trajectories, run in parallel. These systems are associated with a high computational cost and often involve statistical post-processing steps to inexpensively improve their raw prediction qualities. We propose a mixed model that uses only a subset of the original weather trajectories combined with a post-processing step using deep neural networks. These enable the model to account for non-linear relationships that are not captured by current numerical models or post-processing methods. Applied to the global data, our mixed models achieve a relative improvement in ensemble forecast skill (CRPS) of over 14%. https://www.selleckchem.com/products/nsc-23766.html Furthermore, we demonstrate that the improvement is larger for extreme weather events on select case studies. We also show that our post-processing can use fewer trajectories to achieve comparable results to the full ensemble.